WGCNA Modules Exploratory Analysis

#setwd('/afs/inf.ed.ac.uk/user/s17/s1725186/Documents/PhD-Models/FirstPUModel/RMarkdowns')

library(tidyverse) ; library(reshape2) ; library(glue) ; library(plotly) ; library(dendextend)
library(RColorBrewer) ; library(viridis) ; require(gridExtra) ; library(GGally)
suppressWarnings(suppressMessages(library(WGCNA)))
library(expss)
library(polycor)
library(foreach) ; library(doParallel)

SFARI_colour_hue = function(r) {
  pal = c('#FF7631','#FFB100','#E8E328','#8CC83F','#62CCA6','#59B9C9','#b3b3b3','#808080','gray','#d9d9d9')[r]
}

Load preprocessed dataset (preprocessing code in 19_10_14_data_preprocessing.Rmd) and clustering (pipeline in 19_10_21_WGCNA.Rmd)

# Gandal dataset
load('./../Data/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
DE_info = DE_info %>% data.frame


# GO Neuronal annotations: regex 'neuron' in GO functional annotations and label the genes that make a match as neuronal
GO_annotations = read.csv('./../Data/genes_GO_annotations.csv')
GO_neuronal = GO_annotations %>% filter(grepl('neuron', go_term)) %>% 
              mutate('ID'=as.character(ensembl_gene_id)) %>% 
              dplyr::select(-ensembl_gene_id) %>% distinct(ID) %>%
              mutate('Neuronal'=1)


# SFARI Genes
SFARI_genes = read_csv('./../../../SFARI/Data/SFARI_genes_08-29-2019_w_ensembl_IDs.csv')
SFARI_genes = SFARI_genes[!duplicated(SFARI_genes$ID) & !is.na(SFARI_genes$ID),]


# Clusterings
clusterings = read_csv('./../Data/clusters.csv')


# Update DE_info with SFARI and Neuronal information
genes_info = DE_info %>% mutate('ID'=rownames(.)) %>% left_join(SFARI_genes, by='ID') %>% 
  mutate(`gene-score`=ifelse(is.na(`gene-score`), 'None', `gene-score`)) %>%
  left_join(GO_neuronal, by='ID') %>% left_join(clusterings, by='ID') %>%
  mutate(Neuronal=ifelse(is.na(Neuronal), 0, Neuronal)) %>%
  mutate(gene.score=ifelse(`gene-score`=='None' & Neuronal==1, 'Neuronal', `gene-score`), 
         significant=padj<0.05 & !is.na(padj))


rm(DE_info, GO_annotations, clusterings)

---

Dynamic Tree vs Dyamic Hybrid

print(paste0('Dynamic Tree leaves ', sum(genes_info$DynamicTree=='gray'), ' genes without cluster (', 
             round(mean(genes_info$DynamicTree=='gray')*100), '%)'))

## [1] "Dynamic Tree leaves 4208 genes without cluster (26%)"

print(paste0('Dynamic Hybrid leaves ', sum(genes_info$DynamicHybrid=='gray'), ' genes without cluster (', 
             round(mean(genes_info$DynamicHybrid=='gray')*100,2), '%)'))

## [1] "Dynamic Hybrid leaves 113 genes without cluster (0.7%)"

Dynamic Tree leaves many more genes without a cluster, but in previous experiments it returned cleaner results, so I’m going to see which genes are lost to see how big the damage is.

There seems to be a relation between DE and module membership, being DE a more restrictive condition than being assigned to a cluster.

pca = datExpr %>% prcomp

plot_data = data.frame('ID'=rownames(datExpr), 'PC1' = pca$x[,1], 'PC2' = pca$x[,2]) %>%
            left_join(genes_info, by='ID') %>% mutate('hasCluster'=DynamicTree!='gray', 
                                                      'hasSFARIScore'=`gene-score`!='None') %>%
            apply_labels(`gene-score`='SFARI Gene score', DynamicTree = 'Dynamic Tree Algorithm', 
                         significant = 'Differentially Expressed', hasCluster = 'Belongs to a Module',
                         hasSFARIScore = 'Has a SFARI Score', syndromic = 'Has syndromic tag')

p1 = plot_data %>% ggplot(aes(PC1, PC2, color=hasCluster)) + geom_point(alpha=0.2) + 
  theme_minimal() + ggtitle('Genes are assigned to a cluster') + theme(legend.position='bottom')

p2 = plot_data %>% ggplot(aes(PC1, PC2, color=significant)) + geom_point(alpha=0.2) + 
  theme_minimal() + ggtitle('Genes found to be DE') + theme(legend.position='bottom')

grid.arrange(p1, p2, nrow=1)

rm(pca, p1, p2)

Most of the genes that don’t have a cluster are not differentially expressed

cat(paste0(round(100*sum(!plot_data$hasCluster & !plot_data$significant)/sum(!plot_data$hasCluster)),
           '% of the genes that don\'t have a cluster are not differentially expressed\n'))

## 98% of the genes that don't have a cluster are not differentially expressed

cro(plot_data$significant, list(plot_data$hasCluster, total()))

	Belongs to a Module			#Total
	FALSE	TRUE
Differentially Expressed
FALSE	4140	7508		11648
TRUE	68	4431		4499
#Total cases	4208	11939		16147

Most of the genes with a SFARI score are assigned to a cluster

cat(paste0(sum(plot_data$hasSFARIScore & !plot_data$hasCluster), ' of the SFARI genes (~',
           round(100*sum(plot_data$hasSFARIScore & !plot_data$hasCluster)/sum(plot_data$hasSFARIScore)),
           '%) are not assigned to any cluster\n'))

## 151 of the SFARI genes (~17%) are not assigned to any cluster

cro(plot_data$hasSFARIScore, list(plot_data$hasCluster, total()))

	Belongs to a Module			#Total
	FALSE	TRUE
Has a SFARI Score
FALSE	4057	11188		15245
TRUE	151	751		902
#Total cases	4208	11939		16147

Conclusion:

The main ndifference between algorithms is that Dynamic Hybrid clusters outlier genes and Dynamic Tree leaves them out, so Dynamic Tree would give me a ‘cleaner’ group of genes to work with, without losing many SFARI genes, but Dynamic Hybrid has less and more balanced clusters.

I think both options could be feasible, but I’m going to use the Dynamic Hybrid algorithm to keep more genes.

clustering_selected = 'DynamicHybrid'
genes_info$Module = genes_info[,clustering_selected]

---

Dynamic Hybrid Modules

*The colour of the modules is the arbitrary one assigned during the WGCNA algorithm, where the gray cluster actually represents all the genes that were left without a cluster (so it’s not actually a cluster).

cat(paste0('The Dynamic Hybrid algorithm created ', length(unique(genes_info$Module))-1, ' modules and leaves ',
           sum(genes_info$Module=='gray'), ' genes without a module.\n'))

## The Dynamic Hybrid algorithm created 54 modules and leaves 113 genes without a module.

table(genes_info$Module)

## 
## #00A8FF #00ADFA #00B2F4 #00B6EC #00B80F #00B9E3 #00BA38 #00BBDA #00BC50 
##     270     190     154      39      52    1733     231     241     145 
## #00BD63 #00BECF #00BF74 #00BFC4 #00C083 #00C092 #00C0B9 #00C19F #00C1AC 
##     188     291     153     304      41     112     334     414     382 
## #2EA2FF #41B500 #5EB300 #619CFF #73B000 #8195FF #84AD00 #93AA00 #998EFF 
##      33     206      89     459    1461      40     891     162     247 
## #A0A600 #ACA300 #AE87FF #B79F00 #BF80FF #C19B00 #CA9700 #CE79FF #D39200 
##     186     191      32     174     141     301     267     659     249 
## #DB72FB #DB8E00 #E28900 #E56CF4 #E88526 #EE67EC #EE8045 #F37B5A #F564E3 
##     502      55     330     267     215      71     884      49     212 
## #F8766D #FA62DA #FC727E #FE61CF #FE6D8D #FF61C3 #FF63B7 #FF66AA #FF699C 
##      34     158     153     315     181      98      37     996     415 
##    gray 
##     113

plot_data = table(genes_info$Module) %>% data.frame %>% arrange(desc(Freq))

ggplotly(plot_data %>% ggplot(aes(x=reorder(Var1, -Freq), y=Freq)) + geom_bar(stat='identity', fill=plot_data$Var1) + 
         ggtitle('Module size') + ylab('Number of genes') + xlab('Module') + theme_minimal() + 
         theme(axis.text.x = element_text(angle = 90)))

Relation to external clinical traits

Quantifying module-trait associations

In the WGCNA documentation they use Pearson correlation to calculate correlations, I think all of their variables were continuous. Since I have categorical variables I’m going to use the hetcor function, that calculates Pearson, polyserial or polychoric correlations depending on the type of variables involved.

• I’m not sure how the corPvalueStudent function calculates the p-values and I cannot find any documentation…

• Compared correlations using Pearson correlation and with hetcor and they are very similar, but a bit more extreme with hetcor. The same thing happens with the p-values.

datTraits = datMeta %>% dplyr::select(Diagnosis, Region, Sex, Age, PMI, RNAExtractionBatch) %>%
            dplyr::rename('ExtractionBatch' = RNAExtractionBatch)

# Recalculate MEs with color labels
ME_object = datExpr %>% t %>% moduleEigengenes(colors = genes_info$Module)
MEs = orderMEs(ME_object$eigengenes)

# Calculate correlation between eigengenes and the traits and their p-values
moduleTraitCor = MEs %>% apply(2, function(x) hetcor(x, datTraits)$correlations[1,-1]) %>% t
rownames(moduleTraitCor) = colnames(MEs)
colnames(moduleTraitCor) = colnames(datTraits)
moduleTraitPvalue = corPvalueStudent(moduleTraitCor, nrow(datExpr))

# Create text matrix for the Heatmap
textMatrix = paste0(signif(moduleTraitCor, 2), ' (', signif(moduleTraitPvalue, 1), ')')
dim(textMatrix) = dim(moduleTraitCor)

# In case there are any NAs
if(sum(!complete.cases(moduleTraitCor))>0){
  print(paste0(sum(is.na(moduleTraitCor)),' correlation(s) could not be calculated')) 
}

rm(ME_object)

Modules have very strong correlations with Diagnosis with really small p-values and not much relation with anything else. Perhaps a little with PMI and Brain Region.

It’s a good sign that the gray module has one of the lowest correlations with diagnosis, since we know its composed mainly of not differentially expressed genes.

# Sort moduleTraitCor by Diagnosis
moduleTraitCor = moduleTraitCor[order(moduleTraitCor[,1], decreasing=TRUE),]
moduleTraitPvalue = moduleTraitPvalue[order(moduleTraitCor[,1], decreasing=TRUE),]

# Create text matrix for the Heatmap
textMatrix = paste0(signif(moduleTraitCor, 2), ' (', signif(moduleTraitPvalue, 1), ')')
dim(textMatrix) = dim(moduleTraitCor)


labeledHeatmap(Matrix = moduleTraitCor, xLabels = names(datTraits), yLabels =  gsub('ME','',rownames(moduleTraitCor)), 
               yColorWidth=0, colors = brewer.pal(11,'PiYG'), bg.lab.y = gsub('ME','',rownames(moduleTraitCor)),
               textMatrix = textMatrix, setStdMargins = FALSE, cex.text = 0.8, cex.lab.y = 0.75, zlim = c(-1,1),
               main = paste('Module-Trait relationships'))

diagnosis_cor = data.frame('Module' = gsub('ME','',rownames(moduleTraitCor)),
                           'MTcor' = moduleTraitCor[,'Diagnosis'],
                           'MTpval' = moduleTraitPvalue[,'Diagnosis'])

genes_info = genes_info %>% left_join(diagnosis_cor, by='Module')

rm(moduleTraitCor, moduleTraitPvalue, textMatrix, diagnosis_cor)

Modules with a high Module-Diagnosis (absolute) correlation should have a high content of differentially expressed genes

plot_data = genes_info %>% group_by(Module, MTcor) %>% summarise(p = 100*mean(significant))

plot_data %>% ggplot(aes(MTcor, p)) + geom_hline(yintercept=mean(plot_data$p), color='gray', linetype='dotted') +
         geom_point(color=plot_data$Module, aes(id=Module)) + theme_minimal() + 
         xlab('Modules ordered by Module-Diagnosis correlation') + ylab('Percentage of differentially expressed genes')

Gene Significance and Module Membership

Gene significance: is the value between the correlation between the gene and the trait we are interested in. A positive gene significance means the gene is overexpressed and a negative value means its underexpressed. (The term ‘significance’ is not very acurate because it’s not actually measuring statistical significance, it’s just a correlation, but that’s how they call it in WGCNA…)

Module Membership is the correlation of the module’s eigengene and the expression profile of a gene. The higher the Module Membership, the more similar the gene is to the genes that constitute the module. (I won’t use this measure yet)

# It's more efficient to iterate the correlations one by one, otherwise it calculates correlations between the eigengenes and also between the genes, which we don't need

# Check if MM information already exists and if not, calculate it
if(file.exists(paste0('./../Data/dataset_', clustering_selected, '.csv'))){
  
  dataset = read.csv(paste0('./../Data/dataset_', clustering_selected, '.csv'))
  dataset$Module = dataset[,clustering_selected]
  
} else {
  
  ############# 1. Calculate Gene Significance
  GS_info = data.frame('ID' = rownames(datExpr),
                       'GS' = datExpr %>% apply(1, function(x) hetcor(x, datMeta$Diagnosis)$correlations[1,2])) %>%
            mutate('GSpval' = corPvalueStudent(GS, ncol(datExpr)))
  
  #############  2. Calculate Module Membership
  
  #setup parallel backend to use many processors
  cores = detectCores()
  cl = makeCluster(cores-1)
  registerDoParallel(cl)
  
  # Create matrix with MM by gene
  MM = foreach(i=1:nrow(datExpr), .combine=rbind) %dopar% {
    library(polycor)
    tempMatrix = apply(MEs, 2, function(x) hetcor(as.numeric(datExpr[i,]), x)$correlations[1,2])
    tempMatrix
  }
  
  # Stop clusters
  stopCluster(cl)
  
  rownames(MM) = rownames(datExpr)
  colnames(MM) = paste0('MM',gsub('ME','',colnames(MEs)))
  
  # Calculate p-values
  MMpval = MM %>% corPvalueStudent(ncol(datExpr)) %>% as.data.frame
  colnames(MMpval) = paste0('MMpval', gsub('ME','',colnames(MEs)))
  
  MM = MM %>% as.data.frame %>% mutate(ID = rownames(.))
  MMpval = MMpval %>% as.data.frame %>% mutate(ID = rownames(.))
  
  # Join and save results
  dataset = genes_info %>% dplyr::select(ID, `gene-score`, clustering_selected, MTcor, MTpval) %>%
            left_join(GS_info, by='ID') %>%
            left_join(MM, by='ID') %>%
            left_join(MMpval, by='ID')
  
  write.csv(dataset, file = paste0('./../Data/dataset_', clustering_selected, '.csv'), row.names = FALSE)
  
  rm(cores, cl) 
  
}

## Warning in polyserial(y, x, ML = ML, std.err = std.err, bins = bins):
## initial correlation inadmissible, -1.00181903417321, set to -0.9999

## Warning in hetcor.data.frame(dframe, ML = ML, std.err = std.err, use = use, : could not compute polyserial correlation between variables 2 and 1
##     Message: Error in optim(rho, f, control = control, hessian = TRUE, method = "BFGS") : 
##   initial value in 'vmmin' is not finite

## Warning in polyserial(y, x, ML = ML, std.err = std.err, bins = bins):
## initial correlation inadmissible, 1.00437457975294, set to 0.9999

## Warning in hetcor.data.frame(dframe, ML = ML, std.err = std.err, use = use, : could not compute polyserial correlation between variables 2 and 1
##     Message: Error in optim(rho, f, control = control, hessian = TRUE, method = "BFGS") : 
##   initial value in 'vmmin' is not finite

## Warning: Column `ID` joining character vector and factor, coercing into
## character vector

GS_missing = dataset$ID[is.na(dataset$GS)] %>% as.character

if(length(GS_missing)>0){
  
  print(paste0(length(GS_missing),' correlations between genes and Diagnosis could not be calculated, ',
               'calculating them with the polyserial function'))
  
  for(g in GS_missing){
    dataset$GS[dataset$ID == g] = polyserial(as.numeric(datExpr[g,]), datMeta$Diagnosis)
  }
  
}

## [1] "2 correlations between genes and Diagnosis could not be calculated, calculating them with the polyserial function"

## Warning in polyserial(as.numeric(datExpr[g, ]), datMeta$Diagnosis): initial
## correlation inadmissible, -1.00181903417321, set to -0.9999

## Warning in polyserial(as.numeric(datExpr[g, ]), datMeta$Diagnosis): initial
## correlation inadmissible, 1.00437457975294, set to 0.9999

rm(GS_missing)

Analysing concordance between these metrics in the genes

1. Gene Significance vs Log Fold Change

Gene significance and Log Fold Chance are two different ways to measure the same thing, so there should be a concordance between them

Log Fold Chance has some really big outliers, but both variables agree with each other quite well

plot_data = dataset %>% dplyr::select(ID, MTcor, GS) %>% left_join(genes_info %>% dplyr::select(ID, gene.score), by='ID') %>%
            left_join(genes_info %>% dplyr::select(ID, baseMean, log2FoldChange, significant, Module), by='ID') %>%
            left_join(data.frame(MTcor=unique(dataset$MTcor)) %>% arrange(by=MTcor) %>% 
                                 mutate(order=1:length(unique(dataset$MTcor))), by='MTcor')

ggplotly(plot_data %>% ggplot(aes(GS, log2FoldChange)) + geom_point(color=plot_data$Module, alpha=0.5, aes(ID=Module)) + 
         geom_smooth(color='gray') + theme_minimal() + xlab('Gene Significance') + 
         ggtitle(paste0('Correlation = ', round(cor(plot_data$log2FoldChange, plot_data$GS)[1], 4))))

2. Module-Diagnosis correlation vs Gene Significance

In general, modules with the highest Module-Diagnosis correlation should have genes with high Gene Significance

Note: For the Module-Diagnosis plots, if you do boxplots, you lose the exact module-diagnosis correlation and you only keep the order, so I decided to compensate this downside with a second plot, where each point is plotted individually using their module’s Module-Diagnosis correlation as the x axis. I think the boxplot plot is easier to understand but the second plot contains more information, so I don’t know which one is better.

plot_data = plot_data %>% arrange(order)

ggplotly(plot_data %>% ggplot(aes(order, GS, group=order)) + geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + theme_minimal() + 
         xlab('Modules ordered by Module-Diagnosis correlation') + ylab('Gene Significance'))

plot_data %>% ggplot(aes(MTcor, GS)) + geom_hline(yintercept=0, color='gray', linetype='dotted') + 
         geom_point(color=plot_data$Module, alpha=0.1, aes(id=ID)) + geom_smooth(color='gray', alpha=0.3) + 
         theme_minimal() + xlab('Module-Diagnosis correlation') + ylab('Gene Significance') + 
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, plot_data$GS)^2,4)))

3. Module-Diagnosis correlation vs Log Fold Change

The same should happen with the Log Fold Change

ggplotly(plot_data %>% ggplot(aes(order, log2FoldChange, group=order)) + geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + 
         theme_minimal() + xlab('Modules ordered by Module-Diagnosis correlation') + ylab('log2FoldChange'))

ggplotly(plot_data %>% ggplot(aes(MTcor, log2FoldChange)) + geom_hline(yintercept=0, color='gray', linetype='dotted') +
         geom_point(color=plot_data$Module, alpha=0.1, aes(id=ID)) + geom_smooth(color='gray', alpha=0.3) + 
         theme_minimal() + xlab('Module-Diagnosis correlation') + ylab('log2FoldChange') + 
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, plot_data$log2FoldChange)^2,4))))

4. Module-Diagnosis vs Mean Expression

In theory, there shouldn’t be a relation between module-diagnosis and mean expression, but in the the exploratory analysis, we saw that the overexpressed genes tended to have lower levels of expression than the overexpressed genes, and this pattern can be seen in these plots where the modules with negative Module-Diagonsis correlation have slightly higher levels of expression than the modules with positive Module-Diagnosis correlation, although this pattern is note very strong and all modules have similar levels of expression.

ggplotly(plot_data %>% ggplot(aes(order, log2(baseMean+1), group=order)) + 
         geom_hline(yintercept=mean(log2(plot_data$baseMean+1)), color='gray', linetype='dotted') +
         geom_boxplot(fill=unique(plot_data$Module)) + theme_minimal() + 
         xlab('Modules ordered by Module-Diagnosis correlation') + ylab('log2(Mean Expression)'))

plot_data %>% ggplot(aes(MTcor, log2(baseMean+1))) + geom_point(alpha=0.2, color=plot_data$Module, aes(id=ID)) + 
         geom_hline(yintercept=mean(log2(plot_data$baseMean+1)), color='gray', linetype='dotted') + 
         geom_smooth(color='gray', alpha=0.3) + theme_minimal() + xlab('Module-Diagnosis correlation') +
         ggtitle(paste0('R^2=',round(cor(plot_data$MTcor, log2(plot_data$baseMean+1))^2,4)))

Conclusion:

All of the variables seem to agree with each other, Modules with a high correlation with Diagnosis tend to have genes with high values of Log Fold Change as well as high values of Gene Significance, and the gray module, which groups all the genes that weren’t assigned to any cluster tends to have a very poor performance in all of the metrics.

SFARI Scores

Since SFARI scores genes depending on the strength of the evidence linking it to the development of autism, in theory, there should be some concordance between the metrics we have been studying above and these scores…

SFARI Scores vs Gene Significance

• SFARI scores 1 to 5 have a lower median than all genes that have a neuronal-related annotation (!)

• The group with the highest Gene Significance is SFARI score 6, which is supposed to be the one with the least amount of evidence suggesting a relation to autism (!)

• SFARI score 1 is the group with the lowest Gene Significance, with a (slightly) lower median than the genes without any type of Neuronal annotation (!)

• Neuronal annotated genes have higher Gene Significance than genes without any neuronal-related annotation (makes sense)

ggplotly(plot_data %>% ggplot(aes(gene.score, abs(GS), fill=gene.score)) + geom_boxplot() + 
         scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() + 
         ylab('abs(Gene Significance)') + xlab('SFARI Scores') + theme(legend.position='none'))

SFARI Scores vs Module-Diagnosis correlation

• The higher the SFARI score, the lower the Module-Trait correlation (!)

• SFARI scores 1 and 2 have significantly lower values of Module-Trait correlation than the rest of the groups (!)

• The group with the highest Module-Diagnosis correlation is SFARI score 6, which is supposed to be the one with the least amount of evidence suggesting a relation to autism (!)

• SFARI score 1 is the group with the lowest Module-Diagonsis correlation, with a median equal to the first quartile of the genes without any type of Neuronal annotation (!)

ggplotly(plot_data %>% ggplot(aes(gene.score, abs(MTcor), fill=gene.score)) + geom_boxplot() + 
         scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) + theme_minimal() + 
         ylab('abs(Module-Diagnosis Correlation)') + xlab('SFARI Scores') + theme(legend.position='none'))

Conclusion:

Not only are SFARI genes not consistent with the other measurements, but they seem to strongly contradict them. There is a big difference between all the metrics created from gene expression analysis and these scores.

Session info

sessionInfo()

## R version 3.6.0 (2019-04-26)
## Platform: x86_64-redhat-linux-gnu (64-bit)
## Running under: Scientific Linux 7.6 (Nitrogen)
## 
## Matrix products: default
## BLAS/LAPACK: /usr/lib64/R/lib/libRblas.so
## 
## locale:
##  [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_GB.UTF-8    
##  [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8   
##  [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] parallel  stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] doParallel_1.0.15     iterators_1.0.12      foreach_1.4.7        
##  [4] polycor_0.7-10        expss_0.10.1          WGCNA_1.68           
##  [7] fastcluster_1.1.25    dynamicTreeCut_1.63-1 GGally_1.4.0         
## [10] gridExtra_2.3         viridis_0.5.1         viridisLite_0.3.0    
## [13] RColorBrewer_1.1-2    dendextend_1.13.3     plotly_4.9.2         
## [16] glue_1.3.1            reshape2_1.4.3        forcats_0.4.0        
## [19] stringr_1.4.0         dplyr_0.8.3           purrr_0.3.3          
## [22] readr_1.3.1           tidyr_1.0.2           tibble_2.1.3         
## [25] ggplot2_3.2.1         tidyverse_1.3.0      
## 
## loaded via a namespace (and not attached):
##   [1] readxl_1.3.1                backports_1.1.5            
##   [3] Hmisc_4.2-0                 plyr_1.8.5                 
##   [5] lazyeval_0.2.2              splines_3.6.0              
##   [7] BiocParallel_1.20.1         crosstalk_1.0.0            
##   [9] GenomeInfoDb_1.22.0         robust_0.4-18.2            
##  [11] digest_0.6.24               htmltools_0.4.0            
##  [13] GO.db_3.10.0                fansi_0.4.1                
##  [15] magrittr_1.5                checkmate_1.9.4            
##  [17] memoise_1.1.0               fit.models_0.5-14          
##  [19] cluster_2.0.8               annotate_1.64.0            
##  [21] modelr_0.1.5                matrixStats_0.55.0         
##  [23] colorspace_1.4-1            blob_1.2.1                 
##  [25] rvest_0.3.5                 rrcov_1.4-7                
##  [27] haven_2.2.0                 xfun_0.8                   
##  [29] crayon_1.3.4                RCurl_1.95-4.12            
##  [31] jsonlite_1.6                genefilter_1.68.0          
##  [33] impute_1.60.0               survival_2.44-1.1          
##  [35] gtable_0.3.0                zlibbioc_1.32.0            
##  [37] XVector_0.26.0              DelayedArray_0.12.2        
##  [39] BiocGenerics_0.32.0         DEoptimR_1.0-8             
##  [41] scales_1.1.0                mvtnorm_1.0-11             
##  [43] DBI_1.1.0                   Rcpp_1.0.3                 
##  [45] xtable_1.8-4                htmlTable_1.13.1           
##  [47] foreign_0.8-71              bit_1.1-15.2               
##  [49] preprocessCore_1.48.0       Formula_1.2-3              
##  [51] stats4_3.6.0                htmlwidgets_1.5.1          
##  [53] httr_1.4.1                  ellipsis_0.3.0             
##  [55] acepack_1.4.1               pkgconfig_2.0.3            
##  [57] reshape_0.8.8               XML_3.99-0.3               
##  [59] farver_2.0.3                nnet_7.3-12                
##  [61] dbplyr_1.4.2                locfit_1.5-9.1             
##  [63] later_1.0.0                 tidyselect_0.2.5           
##  [65] labeling_0.3                rlang_0.4.4                
##  [67] AnnotationDbi_1.48.0        munsell_0.5.0              
##  [69] cellranger_1.1.0            tools_3.6.0                
##  [71] cli_2.0.1                   generics_0.0.2             
##  [73] RSQLite_2.2.0               broom_0.5.4                
##  [75] fastmap_1.0.1               evaluate_0.14              
##  [77] yaml_2.2.0                  knitr_1.24                 
##  [79] bit64_0.9-7                 fs_1.3.1                   
##  [81] robustbase_0.93-5           nlme_3.1-139               
##  [83] mime_0.9                    xml2_1.2.2                 
##  [85] compiler_3.6.0              rstudioapi_0.10            
##  [87] reprex_0.3.0                geneplotter_1.64.0         
##  [89] pcaPP_1.9-73                stringi_1.4.6              
##  [91] lattice_0.20-38             Matrix_1.2-17              
##  [93] vctrs_0.2.2                 pillar_1.4.3               
##  [95] lifecycle_0.1.0             data.table_1.12.8          
##  [97] bitops_1.0-6                httpuv_1.5.2               
##  [99] GenomicRanges_1.38.0        R6_2.4.1                   
## [101] latticeExtra_0.6-28         promises_1.1.0             
## [103] IRanges_2.20.2              codetools_0.2-16           
## [105] MASS_7.3-51.4               assertthat_0.2.1           
## [107] SummarizedExperiment_1.16.1 DESeq2_1.26.0              
## [109] withr_2.1.2                 S4Vectors_0.24.3           
## [111] GenomeInfoDbData_1.2.2      mgcv_1.8-28                
## [113] hms_0.5.3                   grid_3.6.0                 
## [115] rpart_4.1-15                rmarkdown_1.14             
## [117] Cairo_1.5-10                Biobase_2.46.0             
## [119] shiny_1.4.0                 lubridate_1.7.4            
## [121] base64enc_0.1-3